Linear Algebra and the C Language/a066

__NOTOC__ The coefficients of the equation of a parabola. Presentation : A homogeneous linear system with as many equations as unknowns has a nontrivial solution if and only if the determinant of the matrix is zero. Let us calculate the equation of the parabola passing through points P, Q R: c1 y + c2 x^2 + c3 x + c4 = 0 This same equation with the points P(x1,y1) Q(x2,y2) and R(x3,y3): c1 y1 + c2x1^2 + c3x1 + c4 = 0 c1 y2 + c2x2^2 + c3x2 + c4 = 0 c1 y3 + c2x3^2 + c3x3 + c4 = 0 The system of four equations: c1 y + c2 x^2 + c3 x + c4 = 0 c1 y1 + c2x1^2 + c3x1 + c4 = 0 c1 y2 + c2x2^2 + c3x2 + c4 = 0 c1 y3 + c2x3^2 + c3x3 + c4 = 0 The determinant of the system: |y x^2 x 1| |y1 x1^2 x1 1| = 0 |y2 x2^2 x2 1| |y3 x3^2 x3 1| The determinant in C language: |1 1 1 1| |y1 x1^2 x1 1| = 0 |y2 x2^2 x2 1| |y3 x3^2 x3 1| To calculate the coefficients of the equation of the parabola, we use the cofactor expansion along the first row. cof(R1,C1) y + cof(R1,C2) x^2 + cof(R1,C3) x + cof(R1,C4) = 0 This equation gives us the equation of the parobola that passes through the three points P, Q and R. Application dpara.h .............. Temporary h file Delete this file at the end of the session. c00a.c c00b.c